Skip to main content
1 of 2
Will Boney
  • 508
  • 2
  • 7

This is a really late answer, but the answer to your question is "No." As a dual to the Theorem 6 that Thomas Benjamin mentions above (which I believe is a result of Stavi), Janos Makowsky proved that V\v{o}penka's Principle is equivalent to the statement "All logics have a compactness cardinal."

Will Boney
  • 508
  • 2
  • 7